in a Dispersive Medium. 133 



of which the first factor, varying slowly with t, may be 

 regarded as the amplitude of the luminous vibration. 



The condition of constant amplitude at a given time is 

 that mx-\-\{fjb l —fjb2jz shall remain unchanged. Thus the 

 amplitude which is to be found at # = on the screen 

 prevails also behind the screen along the line 



— xjz = i(/*i--/*2)/w, (7) 



so that (7) may be regarded as the angle o£ aberration due 

 to v. It remains to express this angle by means of (5) in 

 terms of the fundamental data. 



When m is zero, the value of /jl is n/V ; and this is true 

 approximately when m is small. Thus, from (5), 



2 -u 9 2 2mv nV/ 1 



/*! ~/*2 



and 



^-^ ~ 2n/V "~ V ■*"! UV 



????' ?i V / J 1 \ 



H-l—P-2 





(8) 



with sufficient approximation. 



Now in (8) the difference V 2 — V] corresponds to a change 

 in the coefficient of t from n + ???r to n — rnv. Hence, denoting 

 the general coefficient of t by cr, of which V is a function, 

 we have 



Y 1 -Y 2 = 2mv.dY/da, 



and (8) may be written 



/j. 1 -fi 2 _ v r a- dv\ /qx 



Again, 

 and thus 



and 



zm 



V = <r/k, U = da/dk, 



a dV _ dV _ ,*dk 



Y da da k da' 



a dY_ad^_Y 

 V da ~ k da ~ U' 



where U is the group-velocity. 

 Accordingly, 



-x\z = v\V (10) 



expresses the aberration angle, as was to be expected. 

 In the present problem the peculiarity impressed is not 



